SOLUTION: what is {{{f(x)=-(1/4)x^2+2x-2}}} in the standard form of a quadratic?

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: what is {{{f(x)=-(1/4)x^2+2x-2}}} in the standard form of a quadratic?      Log On


   

Question 715589: what is f%28x%29=-%281%2F4%29x%5E2%2B2x-2 in the standard form of a quadratic?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Standard form from general form comes by Completing the Square. You ADD and SUBTRACT a square term.

-%281%2F4%29x%5E2%2B2x-2
Factor the first two terms, %28-1%2F4%29%28x%5E2-8x%29-2
Identify the square term to use: %288%2F2%29%5E2=16...
Add and Subtract this square term, %28-1%2F4%29%28x%5E2-8x%2B16%29-2-16%2A%28-1%2F4%29 [did you understand what was done outside of the parentheses?]
Factor the square trinomial and do other arithmetic, highlight%28-%281%2F4%29%28x-4%29%5E2%2B2%29

Function now in standard form, highlight%28f%28x%29=-%281%2F4%29%28x-4%29%5E2%2B2%29